Exercise
With which of the following groups is the automorphism group of the group Z/2Z × Z/2Z isomorphic?
{e}
Z/2Z
Z/3Z
S3
No.
There is an automorphism interchanging (0,1) and (1,0)
No. The map fixing e, and sending
(0,1) to (1,0); (1,0) to (1,1); (1,1) to (1,0)
is an automorphism of order 3.
No. The map
fixing e and (0,1) and
interchanging (1,0) and (1,1),
is an automorphism of order 2.
Right.